Heat Transfer and Mean Structure of a Turbulent Thermal Plume Along a Vertical Isothermal Wall

Abstract

This investigation considers a two-dimensional turbulent thermal plume rising along a smooth vertical wall which is cooled to the ambient temperature. Mean velocity and temperature profiles within the plume, and the heat flux to the wall, were measured for various plume strengths and distances above the source. Integral analysis suggested an approach to local similarity, based on the local values of the thermal energy flux in the plume and the height above the source, at the limit of large Reynolds number where the local skin friction coefficient and Stanton number can be assumed to be nearly constant. The use of the local similarity hypothesis provided correlations for profiles of mean quantities, comparable to similarity correlations observed for other two-dimensional plumes. The wall plume was found to have greater velocities and temperatures than a free-line plume, in spite of direct losses to the wall. The local similarity hypothesis also provided a satisfactory correlation of wall heat transfer rates. The Nusselt number correlation is Nux=1.344Rax*0.18;2×1010<Rax*<6×1012 for Pr = 0.71. This expression is similar to correlations for turbulent natural convection with uniform heat flux, in fact, the present values are within 20 percent of the values found for natural convection with uniform heat flux for this range of Rax*.